Income Taxes - Components of Deferred Income Taxes (Details) - USD ($) $ in Thousands	Jan. 02, 2024	Jan. 03, 2023
Deferred tax assets (liabilities):
Loss carry forwards	$ 45,547	$ 39,339
Deferred franchise revenue	1,968	2,411
Property, equipment and intangible assets	(20,473)	(14,802)
Stock-based compensation	1,872	1,970
Tax credit carry forwards	8,744	7,231
Interest expense	1,935	617
Inventory smallwares	(1,772)	(1,700)
Other accrued expenses	518	391
Operating lease assets	(49,138)	(49,459)
Operating lease liabilities	59,611	59,747
Other	1,606	1,348
Total deferred tax assets	50,418	47,093
Valuation allowance	(50,673)	(47,322)
Net deferred tax liabilities	$ (255)	$ (229)